Neutral current Drell-Yan production in proton-proton collisions at the LHC was studied with the ATLAS detector. The 20.1 inverse femtobarn data set used in this precision measurement was collected in 2012 during which the LHC collided protons at a centre-of-mass energy of 8 TeV. The production rate or differential cross-section was measured in three-dimensions: invariant mass, absolute rapidity, and cosine of the polar angle in the Collins-Soper frame. A measurement of the forward-backward asymmetry was obtained from the differential cross-section by summing over the forward and the backward events and taking their difference. The three-dimensional differential cross-section measurement presented in this dissertation can be used to constrain the invariant mass- and rapidity-dependent parton distribution functions of the proton and the forward-backward asymmetry results can be used to extract a measurement of the weak mixing angle. / Graduate

We present a combined strong and weak lensing analysis of the J085007.6+360428 (J0850) field, which contains the massive cluster Zwicky 1953. This field was selected for its high projected concentration of luminous red galaxies. Using Subaru/Suprime-Cam BVR(c)I(c)i'z' imaging and MMT/Hectospec spectroscopy, we first perform a weak lensing shear analysis to constrain the mass distribution in this field, including the cluster at z = 0.3774 and a smaller foreground halo at z = 0.2713. We then add a strong lensing constraint from a multiply imaged galaxy in the imaging data with a photometric redshift of z approximate to 5.03. Unlike previous cluster-scale lens analyses, our technique accounts for the full three-dimensional mass structure in the beam, including galaxies along the line of sight. In contrast with past cluster analyses that used only lensed image positions as constraints, we use the full surface brightness distribution of the images. This method predicts that the source galaxy crosses a lensing caustic, such that one image is a highly magnified "fold arc" that could be used to probe the source galaxy's structure at ultra-high spatial resolution (< 30 pc). We calculate the mass of the primary cluster to be M-vir = 2.93(-0.65)(+0.71) x 10(15) M-circle dot. with a concentration of C-vir = 3.46(-0.59)(+0.70), consistent with the mass-concentration relation of massive clusters at a similar redshift. The large mass of this cluster makes J0850 an excellent field for leveraging lensing magnification to search for high-redshift galaxies, competitive with and complementary to that of well-studied clusters such as the HST Frontier Fields.

Doctor of Philosophy / Department of Physics / Carlos A. Trallero / Ultra-fast spectroscopy has become a common tool for understanding the structure and dynamics of atoms and molecules, as evidenced by the award of the 1999 Nobel Prize in Chemistry to Ahmed H. Zewail for his pioneering work in femtochemistry. The use of shorter and more energetic laser pulses have given rise to high intensity table-top light sources in the visible and infrared which have pushed spectroscopic measurements of atomic and molecular systems into the strong-field limit. Within this limit, there are unique phenomena that are still not well understood. Many of such phenomena involve a photoionization step. For three decades, there has been a steady investigation of the single ionization of atomic systems in the strong-field regime both experimentally and theoretically. The investigation of the ionization of more complex molecular systems is of great interest presently and will help with the understanding of ultra-fast spectroscopy as a whole. In this thesis, we explore the single ionization of molecules in the presence of a strong electric field. In particular, we study molecular isomer pairs, molecules that are the same elementally, but different structurally. The main goal of this work is to compare the ionization yields of these similar molecular pairs as a function of intensity and gain some insight into what differences caused by their structure contribute to how they ionize in the strong-field limit. Through our studies we explore a wavelength dependence of the photoionization yield in order to move from the multi-photon regime of ionization to the tunneling regime with increasing wavelength. Also, in contrast to our strong-field studies, we investigate isomeric molecules in the weak-field limit through single photon absorption by measuring the total ionization yield as a function of photon energy. Our findings shed light on the complexities of photoionization in both the strong- and weak-field limits and will serve as examples for the continued understanding of single ionization both experimentally and theoretically.

Weak nucleon nucleon couplings are largely unknown because of the involved theoretical and experimental challenges. Theoretically the topic is difficult due to the non-perturbative nature of the strong interaction, which makes calculations of the couplings challenging. Experimentally, the topic is difficult given that 1) the observables are determined by ratios between strong couplings and weak couplings which differ in size by seven orders of magnitude, and 2) theoretically clean and predictable measurements are almost always restricted to simple systems that do not allow for effects that enhance the size of the asymmetry. However parity violation (PV) can be used to separate out the weak part and thus studies of PV in hadronic systems could offer a unique probe of nucleon structure. The n-3He experiment at the Spallation Neutron Source was performed to measure the parity violating asymmetry of the recoil proton momentum kp with respect to the neutron spin in the reaction n + 3He ---> p + T + 764 keV. This asymmetry is sensitive to the isospin-conserving and isospin-changing (∆I = 0, 1, 2) parts of the Hadronic Weak Interaction (HWI), and is expected to be small (~10-7). The goal of this experiment was to determine this PV asymmetry with a statistical sensitivity of 2x10-8. We also measured the parity even nuclear asymmetry proportional to kp · σn x kn for the first time for verification of nuclear theory and for confirmation of the sensitivity of our experiment to the parity violating asymmetry.

This thesis encompasses a collection of four pieces of work on wave-particle duality, weak-value-assisted tomography, high-dimensional quantum key distribution, and phase-only holograms. In the work on duality, we derive a novel duality relation, and we sketch a thought experiment that leads to an apparent violation of the duality principle. In the project on tomography, we perform a state determination procedure with weak values, and we study the accuracy of the method. In the quantum cryptography project, we optimize an experimental implementation of a quantum cryptography system where two parties share information with the orbital angular momentum degree of freedom of entangled photon pairs. Finally, in the work on holography, we establish the exact solution to the encryption of a phase-only hologram, and experimentally demonstrate its application to spatial light modulators. The four projects provide improvements on measurement procedures in applied and fundamental quantum mechanics.

We study weak convergence of sequences in Banach spaces. In particular, we compare the notions of weak and norm convergence. Although these modes of convergence usually differ, we show that in ℓ¹ they coincide. We then show a theorem of Rosenthal's which states that if {𝓍ₙ} is a bounded sequence in a Banach space, then {𝓍ₙ} has a subsequence {𝓍'ₙ} satisfying one of the following two mutually exclusive alternatives; (i) {𝓍'ₙ} is weakly Cauchy, or (ii) {𝓍'ₙ} is equivalent to the unit vector basis of ℓ¹.

This master´s thesis deals with testing the efficiency of capital markets. The subject to verification of the stock markets of Austria, Hungary, Germany, Great Britain, Czech Republic and Poland during the 2006-2016Q1. The aim of this work is to test the weak formo f efficiency in these markets. The hypothesis was tested using the ACF test ADF and KPSS tests, variance ratio test, run test and test of January effect.

Orientador: Marcelo Martins dos Santos / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatística e Computação Científica / Made available in DSpace on 2018-08-14T14:51:49Z (GMT). No. of bitstreams: 1 Teixeira_EdsonJose_M.pdf: 638751 bytes, checksum: 1d26a9bbc1ee3ba6c4ee45e29c14c45e (MD5) Previous issue date: 2009 / Resumo: Este trabalho consiste de uma exposição detalhada do resultado provado no artigo "Global weak solutions to 1D compressible isentropic Navier-Stokes equations with density-dependent viscosity" de S. Jiang, Z. P. Xin e P. Zhang (Methods Appl. Anal. - 2005), sobre a existência e unicidade de solução fraca para o sistema de Navier-Stokes unidimensional de um fluido isentrópico compressível com viscosidade dependente da densidade e com fronteira livre em coordenadas lagrangianas, ?t +?2ux = 0 0 < x < 1, t > 0 ut + (P(?))x = (?µ (?)ux)x 0 < x < 1, t > 0 onde ?, u; P(?) e µ(?) são a densidade, velocidade, pressão e viscosidade do fluido, e exigiremos que este fluido satisfaça a condição de fronteira (-P(?) + (?µ(?)ux)= 0. Trataremos do caso particular onde consideramos P(?) = A ?? e µ( ?) = B?a; onde A, B > 0,? > 1 e 0 < a < 1 são constantes. Acrescentaremos uma condicão inicial (?0,u0). / Abstract: The present work makes a well-detailed exposition about the main results given in the paper "Global weak solutions to 1D compressible isentropic Navier-Stokes equations with densitydependent viscosity" by S. Jiang, Z. P. Xin and P. Zhang (Methods Appl. Anal. - 2005). The problem in this paper has a free boundary but in lagrangian coordinates the equations are the following, ?t +?2ux = 0 0 < x < 1, t > 0 ut + (P(?))x = (?µ (?)ux)x 0 < x < 1, t > 0 and the boundary becomes the fixed points x = 0 and x = 1; Here ?, u; P(?) and µ(?) are, respectively, the density, velocity, pressure and the viscosity of the fluid. The boundary condition, at x = 0 and x = 1, is given by (-P(?) + (?µ(?)ux)= 0. Although the pressure and viscosity may have more general forms, to be more specific, the authors consider only the special case P(?) = A ?? e µ( ?) = B?a, with A; B > 0,? > 1 and 0 <a< 1 being constants. An initial condition (?0,u0) is also given at time t = 0. / Mestrado / Analise, Equações Diferenciais Parciais / Mestre em Matemática

Orientador: Luís Eduardo Evangelista de Araujo / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-28T09:20:19Z (GMT). No. of bitstreams: 1 Santana_OctavioJoseSantosde_M.pdf: 3448778 bytes, checksum: 7217b98747d619e694a9b6c7b21e9f36 (MD5) Previous issue date: 2015 / Resumo: Um feixe de luz, após sofrer uma reexão em uma interface plana, é deslocado do caminho previsto pela ótica geométrica. Este desvio do feixe é muito pequeno, tipicamente da ordem do comprimento de onda da luz, que é muito menor do que o tamanho do feixe. Portanto, é difícil de se medir. A técnica de medição fraca óptica tem sido utilizada com sucesso em investigações de deslocamentos de feixe, tal como o deslocamento Goos-Hänchen (GH) e o deslocamento Imbert-Fedorov (IF) (esses são deslocamentos longitudinal e perpendicular ao plano de incidência, respectivamente). Em uma medição fraca, o sistema de medida é projetado sobre um determinado estado nal (pós-seleção), quase ortogonal ao estado inicial (pré-seleção), dando origem a um valor fraco que pode assumir valores muito grandes (amplicados). Nesta dissertação estudamos experimentalmente o deslocamento Goos-Hänchen de um feixe gaussiano focalizado ao sofrer reexão interna total em um prisma via medida fraca. Investigamos este efeito em torno do ângulo crítico c para reflexão interna total. Nosso experimento demonstra pela primeira vez que há uma dependência axial do valor fraco que tem que ser levado em conta, além de um fator fenomenológico na equação de correção do valor fraco. Comparações entre os dados com e sem o fator fenomenológico foi feita, mostrando que ao utilizar esse fator, nossos resultados experimentais mostram um excelente acordo com a previsão teórica / Abstract: A beam of light, after reection from a planar interface, is shifted from the path predicted by ray optics. Such a beam shift is very small, typically of the order of the wavelength of light, which is much smaller than the physical size of the beam. Therefore, it is dicult to measure. The optical weak measurement technique has been successfully used in investigations of beam displacements such as the Goos-Hänchen (GH) and the Imbert-Fedorov (IF) shifts (these are longitudinal and perpendicular to the plane of incidence, respectively). In a weak measurement, the measured system is projected onto a certain nal state (postselected), nearly orthogonal to the inicial state (preselected), giving rise to a measured weak value that may take on very large (amplied). In this dissertation, we study experimentally the Goos-Hänchen shift of a focused Gaussian ligth beam undergoing total internal reection in a prism via weak measurement. We investigate this eect near the critical angle c for total internal reection. Our experiment demonstrates for the rst time that there is an axial dependence of the weak value that has to be taken into account, plus a phenomenological factor in the correction equation of the weak value. Comparisons between the data with and without the phenomenological factor was made, showing that by using this factor, our experimental results show an excellent agreement with the theoretical predication / Mestrado / Física / Mestre em Física / 1186838/2013 / CAPES

Dans cette thèse, on étudie le phénomène de localisation d'Anderson des opérateurs de Schrödinger à N particules qui englobe aussi bien la localisation exponentielle des fonctions propres que la localisation dynamique. Dans un premier temps, on considère le modèle d'Anderson discret multi- particulaire avec un potentiel aléatoire à valeurs indépendantes et identiquement distribuées i.i.d. dont la distribution commune est au moins log-Höldérienne et une interaction de courte portée. On établit pour ce modèle la localisation d'Anderson pour les énergies susamment proches du bas du spectre après avoir montré qu'il est non-aléatoire. D'autre part, on montre que la localisation complète des systèmes mono- particulaires s'étend aux systèmes multi-particulaires ayant une interaction globale susamment faible et pour un désordre arbitraire. Pour ce résultat, l'existence d'une densité bornée de la distribution commune des variables aléatoires i.i.d. est nécessaire et on le montre pour des interactions ayant une forme très générale mais bornées. Les résultats sont démontrés à l'aide de l'adaptation aux systèmes multi- particulaires de l'analyse multi-échelle à énergie variable qui permet de traiter des distributions singulières contrairement à la méthode des moments fractionnaires. Les estimées de Wegner intervenant notamment dans l'analyse multi-échelle sont établies pour des cubes vériant une propriété de séparabilité en utilisant le Lemme de Stollmann. On démontre également l'estimée de Combes-Thomas qui joue un rôle important dans l'analyse des énergies extrêmes. / In this thesis, we study for the N-particles Schrodinger operators the Anderson localization phenomenon which consists of both exponential localization of eigenfunctions and dynamical localization. We rst consider the discrete multi-particle Anderson model with a short range interaction and a random potential whose values are independent and identically distributed i.i.d. with a log-Hölder continuous common probability distribution function. For such model, we show that the bottom of its spectrum is non-random and prove the Anderson localization for energies suciently close to the spectral edge. On the other hand, we establish that the complete localization from singleparticle systems extends to multi-particle systems with suciently weak interaction at arbitrary disorder and for absolute continuous probability distribution function of the i.i.d random variables. The results are proved by an adaptation to multi-particle systems of the vari- able energy multi-scale analysis which allows singular distributions instead of the fractional moments method. Wegner bounds, useful for the multi-scale analysis are proved for separable cubes using the Stollmann's Lemma. We also prove the Combes-Thomas estimate which plays an important role in the analysis of extreme energies.